The Nolans star died at her home in Surrey on Thursday morning.
A spokesman for the family said: "Bernie passed away peacefully this morning with all of her family around her.
"The entire family are devastated to have lost beloved Bernie, a wonderful wife, adoring mother and loving sister, she is irreplaceable.
"They kindly ask people to respect their privacy at this difficult time."
Bernie Nolan had revealed in October she was fighting the disease again, just two years after doctors gave her the all-clear from breast cancer.
In February, she was rushed to hospital with a suspected blood clot on her lungs and was told she was nearing the end of her life.
Initially the singer was moved to a hospice, but she then decided to live out the remainder of her days at her family home.
She is survived by her husband Stephen and her 14-year-old daughter Erin.
Born in Dublin but raised in Blackpool, she was the lead singer of 70s pop group The Nolans, along with her sisters Coleen, Linda, Maureen, Anne and Denise.
The group had a number of UK hit singles, including I'm In The Mood For Dancing, Don't Make Waves and Attention to Me.
The Nolans were a well-loved pop group who sold millions of records worldwide, especially in Japan where they sold over 9 million albums.
Bernie Nolan also turned her hand at acting and appeared in popular programmes such as Brookside and The Bill.
Following her death on Thursday a number of Twitter users took to the social networking site to express their condolences.
ITV Daybreak presenter Lorraine Kelly wrote on her Twitter page: "Bernie Nolan was a very special woman brave, funny and hugely talented. She will be sorely missed thoughts with her family and friends."
Former Loose Women presenter Kate Thornton wrote: "Devastated to hear about the sad passing of Bernie Nolan. She was beautiful and inspiring. Thoughts with Coleen Nolan and all her family."